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Novel Methods in Computational Finance

  • Matthias Ehrhardt
  • Michael Günther
  • E. Jan W. ter Maten

Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 25)

Also part of the The European Consortium for Mathematics in Industry book sub series (TECMI, volume 25)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Modelling

    1. Front Matter
      Pages 1-1
    2. Ansgar Jüngel, Lara Trussardi
      Pages 17-29
    3. Nicola Cantarutti, João Guerra, Manuel Guerra, Maria do Rosário Grossinho
      Pages 31-46
    4. Jörg Kienitz
      Pages 47-63
    5. Mark Beinker, Sebastian Schlenkrich
      Pages 65-82
    6. Long Teng, Matthias Ehrhardt, Michael Günther
      Pages 83-105
  3. Analysis

    1. Front Matter
      Pages 107-107
    2. Ljudmila A. Bordag, Ivan P. Yamshchikov
      Pages 109-128
  4. Transformation Methods and Special Discretizations

    1. Front Matter
      Pages 169-169
    2. Rafael Company, Vera N. Egorova, Mohamed El Fakharany, Lucas Jódar, Fazlollah Soleymani
      Pages 171-214
    3. Miglena N. Koleva, Radoslav L. Valkov
      Pages 215-226
  5. Numerical Methods in Finance

    1. Front Matter
      Pages 227-227
    2. Shih-Hau Tan, Choi-Hong Lai
      Pages 229-242
    3. Álvaro Leitao, Lech A. Grzelak, Cornelis W. Oosterlee
      Pages 253-263
    4. Jörg Kienitz, Thomas McWalter, Roelof Sheppard
      Pages 265-291
  6. Compact FDMs and Splitting Schemes

    1. Front Matter
      Pages 293-293
    2. Bertram Düring, Christian Hendricks, James Miles
      Pages 295-312
    3. Miglena N. Koleva, Walter Mudzimbabwe, Lubin G. Vulkov
      Pages 321-331
    4. Zuzana Bučková, Matthias Ehrhardt, Michael Günther, Pedro Pólvora
      Pages 333-371
    5. Karel in ’t Hout, Radoslav L. Valkov
      Pages 373-398
    6. Christian Hendricks, Christof Heuer, Matthias Ehrhardt, Michael Günther
      Pages 399-405
  7. Scientific Computing

    1. Front Matter
      Pages 407-407
    2. Beatrice Gaviraghi, Mario Annunziato, Alfio Borzì
      Pages 409-422
    3. Beatrice Gaviraghi, Mario Annunziato, Alfio Borzì
      Pages 423-439
    4. José P. Silva, E. Jan W. ter Maten, Michael Günther, Matthias Ehrhardt
      Pages 441-452
  8. High Performance Computing

    1. Front Matter
      Pages 453-453
    2. Choi-Hong Lai, André M. S. Ribeiro, Natkunam Kokulan
      Pages 455-463
    3. Álvaro Leitao, Cornelis W. Oosterlee
      Pages 465-476
    4. José Germán López-Salas, Carlos Vázquez Cendón
      Pages 477-500
  9. Software

    1. Front Matter
      Pages 501-501
    2. Paul Bilokon, James Gwinnutt, Daniel Jones
      Pages 503-542
    3. Christof Heuer, Pedro Pólvora, José Silva, Matthias Ehrhardt, Michael Günther, E. Jan W. ter Maten
      Pages 561-601
  10. Back Matter
    Pages 603-606

About this book

Introduction

This book discusses the state-of-the-art and open problems in computational finance. It presents a collection of research outcomes and reviews of the work from the STRIKE project, an FP7 Marie Curie Initial Training Network (ITN) project in which academic partners trained early-stage researchers in close cooperation with a broader range of associated partners, including from the private sector.

The aim of the project was to arrive at a deeper understanding of complex (mostly nonlinear) financial models and to develop effective and robust numerical schemes for solving linear and nonlinear problems arising from the mathematical theory of pricing financial derivatives and related financial products. This was accomplished by means of financial modelling, mathematical analysis and numerical simulations, optimal control techniques and validation of models.

In recent years the computational complexity of mathematical models employed in financial mathematics has witnessed tremendous growth. Advanced numerical techniques are now essential to the majority of present-day applications in the financial industry.

Special attention is devoted to a uniform methodology for both testing the latest achievements and simultaneously educating young PhD students. Most of the mathematical codes are linked into a novel computational finance toolbox, which is provided in MATLAB and PYTHON with an open access license. The bookoffers a valuable guide for researchers in computational finance and related areas, e.g. energy markets, with an interest in industrial mathematics.

Keywords

nonlinear Black-Scholes equations Lie Algebra techniques Lévy methods high-dimensional partial differential equations optimal control techniques calibration positivity preservation artificial boundary condition transformation techniques mixed derivatives correlation model order reduction uncertainty quantification ADI-methods GPU programming

Editors and affiliations

  • Matthias Ehrhardt
    • 1
  • Michael Günther
    • 2
  • E. Jan W. ter Maten
    • 3
  1. 1.Lehrstuhl für Angewandte Mathematik/Numerische AnalysisBergische Universität WuppertalWuppertalGermany
  2. 2.Lehrstuhl für Angewandte Mathematik/Numerische AnalysisBergische Universität WuppertalWuppertalGermany
  3. 3.Lehrstuhl für Angewandte Mathematik/Numerische AnalysisBergische Universität WuppertalWuppertalGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-61282-9
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-61281-2
  • Online ISBN 978-3-319-61282-9
  • Series Print ISSN 1612-3956
  • Series Online ISSN 2198-3283
  • Buy this book on publisher's site
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